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Optimization of simplified grinding wheel geometry for the accurate generation of end-mill cutters using the five-axis CNC grinding process

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Abstract

A simple geometric and optimal method is adopted for the five-axis CNC grinding of the end-mill cutters. In this research, initially a simplified parametric profile of the grinding wheel is constructed using line segments and circular arcs. The equation of the wheel swept-surface in five-axis grinding is derived. Then subjected to the flute profile design, the profile parameters of the grinding wheel, its relative location, and orientation with respect to the end-mill cutter are optimized, ensuring a specified normal rake angle. Finally, validation of the newly developed method has been performed using the CAD simulation; two virtually ground flutes are measured and compared with the given specifications. The normal rake angle is related with the radial rake angle by a relationship established in this work. This innovative approach can determine the non-standard grinding wheel that can be economically produced or dressed to accurately grind the end-mill cutters using the five-axis CNC grinding process.

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Abbreviations

A M :

Angular displacements of the mill-cutter about its axis

B M :

Angular displacements about the carriage assembly rotation axis

Cr :

Crossover probability

D :

Constant of differentiation

DE:

Differential evolution

F(l):

Designed flute profile

F m :

Ground flute profile

I:

Tangent vector of the side-cutting edge at point PC

J:

Vector along the rake face

K:

Cross product of I and J

M:

A plane perpendicular to the end-mill axis

P C :

Point on helical side cutting edge C(θ) on the end-mill cutter

S:

Line formed by intersection between planes Γand Π

T 1 :

Length of line segment oGP1

T 2 :

Length of line segment P1P2

T 3 :

Length of line segment P4P5

P W :

Point with parameter \( \left({u}_{{\mathbf{P}}_{\mathbf{W}}},{v}_{{\mathbf{P}}_{\mathbf{W}}}\right) \) in ℜG coordinate system

R 1 :

Radius of circular arc P2P3

R 2 :

Radius of circular arc P3P4

SV(u, v, t):

Flute surface

WL(x WL, y WL, z WL):

Grinding-wheel location

f 0 f 1 :

Line segment

f 1 f 2 :

Circular arc

f 2 f 3 :

Circular arc

f 3 f 4 :

Line segment

l :

Flute profile parameter

\( {l}_{{\mathbf{f}}_1} \) :

Length of f0f1

\( {l}_{{\mathbf{f}}_2} \) :

Length of curve f1f2

\( {l}_{{\mathbf{f}}_3} \) :

Length of curve f2f3

\( {l}_{{\mathbf{f}}_4{\mathbf{f}}_5} \) :

Length of segment f3f4

\( {l}_{{\mathbf{f}}_5} \) :

Length of segment f4f5

pop :

Main population

rnd :

Random number

r 1 :

Radius of f1f2

r 2 :

Radius of f2f3

t :

Specified rake angle

u :

Parameter of grinding-wheel along its width

v :

Angular parameter of the wheel

v R :

A unit vector passing through the point PC

(x WL. y WL,z WL):

Grinding-wheel location

α n :

Normal rake angle

α R :

Radial rake angle

β 1 :

Angle of line segment P1P2

γ S :

Secondary relief angle

γ P :

Primary relief angle

ψ :

Helix angle

θ :

Rotation angle about zT-axis

μ :

Grinding-wheel rotation about xG-axis

η :

Grinding-wheel rotation about zG-axis

ℜ T ≕ (oTx Ty Tz T):

Tool coordinate system

ℜ G(oGx Gy Gz G):

Grinding-wheel coordinate system

ℜ M(oMx My Mz M):

Machine coordinate system

Γ :

Plane passing through point PC and normal to the cutting edge

Π :

Plane normal to the cutting velocity

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Author information

Authors and Affiliations

  1. Department of Industrial and Manufacturing Engineering (IMD), NED University of Engineering and Technology, Karachi, Pakistan

    Muhammad Wasif, Syed Amir Iqbal, Aqeel Ahmed & Muhammad Tufail

  2. Mechanical Engineering Department, Hashemite University, Zarqa, Jordan

    Mahmoud Rababah

Authors
  1. Muhammad Wasif
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  2. Syed Amir Iqbal
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  3. Aqeel Ahmed
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  4. Muhammad Tufail
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  5. Mahmoud Rababah
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Contributions

All the authors have taken equal part in performing the research and are sequenced their names in consent with each other. In this research,

• A simplified parametric profile of the grinding-wheel is constructed using line segments and circular arcs. The equation of the wheel swept-surface in five-axis grinding is derived.

• Subjected to the flute profile design, the profile parameters of the grinding wheel, its relative location, and orientation with respect to the end-mill cutter are optimized, ensuring a specified normal rake angle.

• Validation of the newly developed method has been performed using the CAD simulation, two virtually ground flutes are measured and compared with the given specifications.

Grinding of end-mill cutter flutes are often achieved through the inverse method, in which a free-form grinding wheel is first determined and manufactured, the grinding wheel is then used to accurately generate the flutes; however, such free-form grinding wheels are very difficult and expensive to manufacture. Moreover, this method neither generates the rake face with the defined normal rake angle accurately nor generates the precise side-cutting edges on the end-mill cutters. To solve this issue, a simple geometric optimization approach is adopted for the multi-axis CNC grinding of the end-mill flutes.

This new approach can determine the non-standard grinding wheel that can be economically produced or dressed to accurately grind the end-mill cutters using the five-axis CNC grinding process.

Corresponding author

Correspondence to Muhammad Wasif.

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All the authors jointly worked together and contributed in the research and there is no conflict of interest applicable to this research or publication of it.

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Wasif, M., Iqbal, S.A., Ahmed, A. et al. Optimization of simplified grinding wheel geometry for the accurate generation of end-mill cutters using the five-axis CNC grinding process. Int J Adv Manuf Technol 105, 4325–4344 (2019). https://doi.org/10.1007/s00170-019-04547-8

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